Y=12x^2-11x-5

Solution for Y=12x^2-11x-5 equation:

=12Y^2-11Y-5

We move all terms to the left:

-(12Y^2-11Y-5)=0

We get rid of parentheses

-12Y^2+11Y+5=0

a = -12; b = 11; c = +5;
Δ = b2-4ac
Δ = 112-4·(-12)·5
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*-12}=\frac{-30}{-24}
=1+1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*-12}=\frac{8}{-24}
=-1/3
$